The BBC was standing by Jeremy Clarkson on Friday night as the furore over his joke that striking public sector workers should be "executed in front of their families" refused to go away, with the number of registered complaints climbing to more than 21,000.

BBC insiders said there would be no "massive inquest" into Clarkson's remarks about public sector strikers on BBC1's The One Show on Wednesday night.

The Top Gear presenter, whose 23-year BBC career is littered with controversy as a result of his forthright views and robust sense of humour, is not thought to be facing any disciplinary action despite a feeling among senior BBC staff that his comments were "beyond the pale".

Clarkson, who flew out to China to film a new series of Top Gear as the row erupted on Thursday, issued an apology that evening after David Cameron, Ed Miliband and public sector union Unison became embroiled in the affair.

The BBC declined on Friday night to provide an update on how many complaints it had received about the comments, but on Friday morning the figure stood at 21,335, up from about 5,000 the previous afternoon.

Clarkson told the Times that a BBC producer had given the green light to his comments. However, it is understood that his discussion was with a relatively junior member of The One Show's research team and his remarks on the live show "went further" than what had been discussed beforehand.

Alex Jones, the show's co-presenter, introduced Clarkson as a guest with "balanced, uncontroversial opinions". Clarkson then went on to say how empty the roads had been because of the strikes, before saying: "We have to balance it though … because this is the BBC."

He then said: "Frankly, I'd have them all shot! I would take them outside and execute them in front of their families. I mean, how dare they go on strike when they've got these gilt-edged pensions that are going to be guaranteed while the rest of us have to work for a living?"

BBC insiders said there was no appetite for sacking Clarkson, who is known to push the boundaries with flippant remarks. Bosses will discuss the saga with Clarkson when he returns to London after Christmas, but insiders insisted there would be "no hauling over the coals".

There is a feeling inside the corporation that the pre-show briefing could have done more to warn Clarkson, but that controversial performers always run the risk of causing a row when asked about topical issues on live TV.

Unlike the "Sachsgate" affair in 2008, which drew 27,000 complaints and led to the resignation of Russell Brand and suspension of Jonathan Ross from the corporation, this time the BBC issued three apologies in less than 48 hours after the broadcast on Wednesday.

"There will be no formal inquisitions," a BBC insider said. "There's only so much you can do on live TV. There is a feeling he went further [than advised]. He knew where the line was and overegged it."

Clarkson said in a statement on Thursday night: "I didn't for a moment intend these remarks to be taken seriously – as I believe is clear if they're seen in context. If the BBC and I have caused any offence, I'm quite happy to apologise for it alongside them."

However, despite the apology, the presenter told the Sun on Friday "there isn't a case to answer" in the context of the full interview. He is understood to have written his weekly Sun column, to be published on Saturday, before the row escalated and it is not known whether he will skirt around the controversy or issue a second defence. "It's a knee-jerk reaction to something where you're only getting part of the story," he told the Sun.

Clarkson's semi-apology prompted criticism from other celebrities. The broadcaster Dame Joan Bakewell told reporters at the Women in Film and Television awards on Friday that his outburst was "outrageous, unforgivable". She added: "I dislike the phrase 'If I have given offence I apologise.' That's a cop-out. What you should say is 'I give unqualified apology' so that's what we'd like to hear."

Dave Prentis, the general secretary of Unison, welcomed Clarkson's climbdown after calling for him to be sacked on Thursday and threatening to report the presenter to the police. Prentis invited Clarkson, one of the BBC's most highly paid stars, to spend a day on hospital wards cleaning up sick and "wiping bottoms". "We think he has many of the personal skills necessary for the job," said Prentis.